Mathematical model for promotion of wound closure with ATP release.

To computationally investigate the recent experimental finding such that extracellular ATP release caused by exogeneous mechanical forces promote wound closure, we introduce a mathematical model, the Cellular Potts Model (CPM), which is a popular discretized model on a lattice, where the movement of a "cell" is determined by a Monte Carlo procedure. In the experiment, it was observed that there is mechanosensitive ATP release from the leading cells facing the wound gap and the subsequent extracellular Ca influx. To model these phenomena, the Reaction-Diffusion equations for extracellular ATP and intracellular Ca concentrations are adopted and combined with CPM, where we also add a polarity term because the cell migration is enhanced in the case of ATP release.

Non-Markov-Type Analysis and Diffusion Map Analysis for Molecular Dynamics Trajectory of Chignolin at a High Temperature.

We apply the non-Markov-type analysis of state-to-state transitions to nearly microsecond molecular dynamics (MD) simulation data at a folding temperature of a small artificial protein, chignolin, and we found that the time scales obtained are consistent with our previous result using the weighted ensemble simulations, which is a general path-sampling method to extract the kinetic properties of molecules. Previously, we also applied diffusion map (DM) analysis, which is one of a manifold of learning techniques, to the same trajectory of chignolin in order to cluster the conformational states and found that DM and relaxation mode analysis give similar results for the eigenvectors. In this paper, we divide the same trajectory into shorter pieces and further apply DM to such short-length trajectories to investigate how the obtained eigenvectors are useful to characterize the conformational change of chignolin.

Multiscale Aspects of Molecular Motions: From Molecular Vibrations, Conformational Changes of Biomolecules to Cellular Dynamics.

Molecular aspects of living systems are important because it is the most basic aspects of life as exemplified in biochemistry and structural biology. Since molecules move due to interactive forces between atoms, physics plays an important role to understand the dynamic phenomena of living systems. Here we review our multiscale approaches for computationally treating different levels of molecular motions: vibrational dynamics of molecules, conformational change of biomolecules, and cellular dynamics using statistical-mechanics-based models.

Path Ensembles for Pin1-Catalyzed Cis-Trans Isomerization of a Substrate Calculated by Weighted Ensemble Simulations.

Pin1 enzyme protein recognizes specifically phosphorylated serine/threonine (pSer/pThr) and catalyzes the slow interconversion of the peptidyl-prolyl bond between cis and trans forms. Structural dynamics between the cis and trans forms are essential to reveal the underlying molecular mechanism of the catalysis. In this study, we apply the weighted ensemble (WE) simulation method to obtain comprehensive path ensembles for the Pin1-catalyzed isomerization process.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions.

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models.

Conformational change of a biomolecule studied by the weighted ensemble method: Use of the diffusion map method to extract reaction coordinates.

We simulate the nonequilibrium ensemble dynamics of a biomolecule using the weighted ensemble method, which was introduced in molecular dynamics simulations by Huber and Kim and further developed by Zuckerman and co-workers. As the order parameters to characterize its conformational change, we here use the coordinates derived from the diffusion map (DM) method, one of the manifold learning techniques. As a concrete example, we study the kinetic properties of a small peptide, chignolin in explicit water, and calculate the conformational change between the folded and misfolded states in a nonequilibrium way.

Energetics and conformational pathways of functional rotation in the multidrug transporter AcrB.

The multidrug transporter AcrB transports a broad range of drugs out of the cell by means of the proton-motive force. The asymmetric crystal structure of trimeric AcrB suggests a functionally rotating mechanism for drug transport. Despite various supportive forms of evidence from biochemical and simulation studies for this mechanism, the link between the functional rotation and proton translocation across the membrane remains elusive.

Extended Phase-Space Methods for Enhanced Sampling in Molecular Simulations: A Review.

Molecular Dynamics simulations are a powerful approach to study biomolecular conformational changes or protein-ligand, protein-protein, and protein-DNA/RNA interactions. Straightforward applications, however, are often hampered by incomplete sampling, since in a typical simulated trajectory the system will spend most of its time trapped by high energy barriers in restricted regions of the configuration space. Over the years, several techniques have been designed to overcome this problem and enhance space sampling.

Reconstruction of semiautomated cardiac regions of interest using iodine-123 metaiodobenzylguanidine myocardial scintigraphy.

Introduction: Analysis using cardiac iodine-123 metaiodobenzylguanidine (MIBG) scintigraphy with regions of interest (ROIs) is useful for assessing myocardial sympathetic activity. However, manual placement of the cardiac ROI is sometimes difficult because myocardial MIBG uptake is reduced in patients with heart failure. A new method was developed to reconstruct the semiautomated cardiac ROI in a sympathetic denervated heart.

Multiscale enhanced path sampling based on the Onsager-Machlup action: application to a model polymer.

We propose a novel path sampling method based on the Onsager-Machlup (OM) action by generalizing the multiscale enhanced sampling technique suggested by Moritsugu and co-workers [J. Chem. Phys.

Minimum free energy path of ligand-induced transition in adenylate kinase.

Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space.

A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates.

We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the "centroid IRC," corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e.

Different inhibitory potency of febuxostat towards mammalian and bacterial xanthine oxidoreductases: insight from molecular dynamics.

Febuxostat, a drug recently approved in the US, European Union and Japan for treatment of gout, inhibits xanthine oxidoreductase (XOR)-mediated generation of uric acid during purine catabolism. It inhibits bovine milk XOR with a K(i) in the picomolar-order, but we found that it is a much weaker inhibitor of Rhodobacter capsulatus XOR, even though the substrate-binding pockets of mammalian and bacterial XOR are well-conserved as regards to catalytically important residues and three-dimensional structure, and both permit the inhibitor to be accommodated in the active site, as indicated by computational docking studies. To clarify the reason for the difference of inhibitory potency towards the two XORs, we performed molecular dynamics simulations.

Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways.

For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method.

Evaluation of utility of asymmetric index for count-based oxygen extraction fraction on dual-tracer autoradiographic method for chronic unilateral brain infarction.

Objective: For diagnosing patients with ischemic cerebrovascular disease, non-invasive count-based method with (15)O(2) and H (2) (15) O positron-emission tomography (PET) data is widely used to measure asymmetric increases in oxygen extraction fraction (OEF). For shortening study time, we have proposed dual-tracer autoradiographic (DARG) protocol in which (15)O(2) gas and C(15)O(2) gas are sequentially administrated within short period. In this paper, we evaluated feasibility of the non-invasive count-based method with the DARG protocol.

Mode-specific vibrational energy relaxation of amide I' and II' modes in N-methylacetamide/water clusters: intra- and intermolecular energy transfer mechanisms.

The mode-specific vibrational energy relaxation of the amide I' and amide II' modes in NMA-d(1)/(D(2)O)(n) (n = 0-3) clusters were studied using the time-dependent perturbation theory at the B3LYP/aug-cc-pvdz level. The amide modes were identified for each cluster based on the potential energy distribution of each mode. The vibrational population relaxation time constants were derived for the amide I' and II' modes.

Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. I. Five-coordinate ferrous iron porphyrin model.

The time scales and mechanisms of mode-specific vibrational energy relaxation in imidazole ligated ferrous iron porphine were studied using a non-Markovian time-dependent perturbation theory and density functional theory calculation. Seven normal modes, including nu(4), nu(7), and five Fe out-of-plane modes (Fe-oop), were treated as the relaxing system mode coupled to all other modes forming the bath. The derived cooling time constants for the nu(4) and nu(7) modes agree well with the results of previous experimental studies.

Dynamic treatment of vibrational energy relaxation in a heterogeneous and fluctuating environment.

A computational approach to describe the energy relaxation of a high-frequency vibrational mode in a fluctuating heterogeneous environment is outlined. Extending previous work [H. Fujisaki, Y.

Vibrational energy relaxation of isotopically labeled amide I modes in cytochrome c: theoretical investigation of vibrational energy relaxation rates and pathways.

With use of a time-dependent perturbation theory, vibrational energy relaxation (VER) of isotopically labeled amide I modes in cytochrome c solvated with water is investigated. Contributions to the VER are decomposed into two contributions from the protein and water. The VER pathways are visualized by using radial and angular excitation functions for resonant normal modes.

Analytic approach for controlling quantum states in complex systems.

We examine random matrix systems driven by an external field in view of optimal control theory (OCT). By numerically solving OCT equations, we can show that there exists a smooth transition between two states called "moving bases" which are dynamically related to initial and final states. In our previous work [J.

Molecular dynamics study on the solvent dependent heme cooling following ligand photolysis in carbonmonoxy myoglobin.

The time scale and mechanism of vibrational energy relaxation of the heme moiety in myoglobin was studied using molecular dynamics simulation. Five different solvent models, including normal water, heavy water, normal glycerol, deuterated glycerol and a nonpolar solvent, and two forms of the heme, one native and one lacking acidic side chains, were studied. Structural alteration of the protein was observed in native myoglobin glycerol solution and native myoglobin water solution.

Efforts toward developing direct probes of protein dynamics.

We report the first IR characterization of a single C-D bond within a protein, methyl-d1 Met80 of horse heart cytochrome c. A comparison was made to methyl-d1/d3 methionine as well as methyl-d3 Met80. We found that for methyl-d1 and the asymmetric stretches of methyl-d3, line widths/line shapes are dominated by inhomogeneous broadening, whereas the symmetric stretch of methyl-d3 has a significant homogeneous component.

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins.

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins.

Dynamical aspects of quantum entanglement for weakly coupled kicked tops.

We investigate how the dynamical production of quantum entanglement for weakly coupled, composite quantum systems is influenced by the chaotic dynamics of the corresponding classical system, using coupled kicked tops. The linear entropy for the subsystem (a kicked top) is employed as a measure of entanglement. A perturbative formula for the entanglement production rate is derived.

Vibrational energy relaxation in proteins.

An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochrome c is studied by using two theoretical approaches. One approach is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach, which describes the protein as an ensemble of normal modes interacting through nonlinear coupling elements.